Limits and Limit Theorems - Basic Calculus PDF

Limits and Limit Theorem Basic Calculus Learning Outcomes Illustrate the limit of a function using a table of values and the graph of the function; Distinguish between lim 𝑓(𝑥) and 𝑓(𝑐) 𝑥→𝑐 Illustrate the limit theorems; and Apply the limit theorems in eval...

Limits and Limit Theorem Basic Calculus Learning Outcomes Illustrate the limit of a function using a table of values and the graph of the function; Distinguish between lim 𝑓(𝑥) and 𝑓(𝑐) 𝑥→𝑐 Illustrate the limit theorems; and Apply the limit theorems in evaluating the limit of algebraic functions (polynomial, rational, and radical). Introduction Limits are the backbone of calculus, and calculus is called the Mathematics of Change. The study of limits is necessary in studying change in great detail. The evaluation of a particular limit is what underlies the formulation of the derivative and the integral of a function. Introduction This is how it is with limits of functions. We will consider functions of a single variable and study the behavior of the function as its variable approaches a particular value (a constant). The variable can only take values very, very close to the constant, but it cannot equal the constant itself. However, the limit will be able to describe clearly what is happening to the function near that constant Limit of a Function using Table of Values and Graph  From the right Introduction  From the left Introduction  From the right Introduction  From the left Introduction  = 2.5 DNE =0 DNE =1 DNE = -1 DNE =5 Activity #1 Limit Theorems Previously, we discussed how limits can be determined through either a table of values or the graph of a function. One might ask: Must one always construct a table or graph the function to determine the limit? Filling in a table of values sometimes requires very tedious calculations. Likewise, a graph may be difficult to sketch. However, these should not be reasons for a student to fail to determine a limit. In this lesson, we will learn how to compute the limit of a function using Limit Theorems. LIMIT OF A LINEAR FUNCTION Application of Limit Theorems Activity #2 References DepEd. 2013. Basic Calculus. Teachers Guide. Lim, Yvette F., Nocon, Rizaldi C., Nocon, Ederlina G., and Ruivivar, Leonar A. 2016. Math for Engagement Learning Grade 11 Basic Calculus. Sibs Publishing House, Inc. Mercado, Jesus P., and Orines, Fernando B. 2016. Next Century Mathematics 11 Basic Calculus. Phoenix Publishing House, Inc. Geogebra. Graphing application for android. Playstore.